To a designer, it is the most practical method in designing an elementary structure of an optical lens that the optical trace of an incident ray in an optic system is obtained by some simple formulae. Such a method calculates and then tracks the optical trace of an incident ray in the optical system by using corresponding refraction and transfer formulae under a paraxial condition thereof.
Paraxial optics deals with the light transmission problem of a centered optical system symmetrical with regard to the axes thereof. Normally, a paraxial optics system includes rotary reflection planes or refraction planes with a common axis, which is called the optical axis. Such a centered optical system has one character that if a ray passes through this system very close to the optical axis, it will intersect with corresponding normal lines of any mirror surfaces within the system thereby resulting in a small angle of incidence. Such a ray is thus called a paraxial ray.
FIG. 1 of the attached drawings gives a simple paraxial optical system. A ray R1 parallel to the optical axis of the paraxial optical system enters a lens L from the left side thereof and intersects with the optical axis at a point F′, which is referred to as a focal point of the lens L (also referred to as a second focal point). Another ray R2 passes through the lens L from a point at the left side thereof and comes out in a way parallel to the optical axis at the same height that the ray R1 enters into the system, which defines a first focal point F1 of the system. The two rays R1 and R2 intersect within the object space at a point O and define a point O′ in the image space. That is, the point O′ is an image of the point O. As the rays enter the lens L at an arbitrary height, the plane containing the point O and vertical to the optical axis forms an image of a corresponding plane containing the point O′ and vertical to the optical axis as well. The two planes intersect with the optical axis respectively at the so-called principal points P and P′. The first principal point P is located in the object space while the second principal point P′ is located in the image space. The point P′ is thus the image of the point P. Moreover, as the distance from the point O to the optical axis equals to that from the point O′ to the optical axis, the lateral magnifying rates of the images are also the same. Hence, the two planes OP and O′P′ are the principal planes of the optical system and have a conjugative relationship therebetween. The distance from the first focal point to the first principal point is named the first focal length, while the distance from the second principal point to the second focal point is referred to as the second focal length or effective focal length (EFL).
U.S. Pat. No. 7,023,622 discloses an objective lens for microscopes. The objective lens comprises a first positive lens, a second positive lens, and a third The objective lens has a numerical aperture greater than or equal to 0.4, and a magnification ranging between 11 and 12 or between 4 and 11. The US patent aims to provide an objective lens that has a relatively small ratio of magnification-to-numerical aperture, for example, less than 30, and has a relative great ratio of the field of view (FOV)-to-diameter at the same time, for example, more than 0.1.
U.S. Pat. No. 6,560,033 also gives an objective lens including, from an object side to an image side thereof, a first meniscus positive lens, a second lens with a positive refractive power, a third lens group with a positive refractive power, a fourth lens group, and a fifth lens group. Such an objective lens system for microscopes has a magnification of 50 and a long working distance with the numerical aperture thereof reaching 0.55.
Still, another conventional objective lens provided by U.S. Pat. No. 6,501,603 adopts Gauss lens sets. This lens comprises a first positive lens group G1 and a second lens group G2. The second lens group G2 has a plurality of Gauss lens sets G2A to G2C. Each of the Gauss lens sets includes, from an object side to an image side thereof, a meniscus-shaped optical element with a concave surface facing the image side and a meniscus-shaped optical element with a concave surface facing the object side. This objective lens aims to take advantage of Gauss lens sets to correct aberrations. However, because more than two Gauss lens sets are used, the overall length and volume of the objective lens are inevitably increased and so do the costs thereof.
FIG. 2 shows a paraxial schematic view of a conventional optical system with a positive focal length. Generally, values of the numerical aperture in the object space (NAO) and the magnification (M) of such a positive optical system are given as follows:
NAOM0.050.90.140.25100.4250.65400.85631.25100
If the magnification has to be between 0.9 and 9, which implies that the scope of the NAO is around 0.05-0.15, then the image resolution of the system is 4.06λ to 12.2λ according to the well-known image resolution formula of microscopes: δ=0.61*λ/NAO. Thus, the result for the image resolution of such a positive optical system is not good.
Furthermore, as to a positive optical system, if it has a high magnification, then the distance between an object and the objective lens is relatively short; and vice versa. Hence, when there is a long distance between an object and the objective lens, the aperture of the lens has to be increased in order to enhance the NAO thereof, thereby adversely affecting the quality of the lens itself. On the contrary, a negative optical system can has a relatively large NAO while having a low magnification. Therefore, it is necessary to design a new negative optical system that has an increased NAO value with the same magnification to thereby enhance the image resolution thereof.